Bayesian smoothing and regression splines for measurement error problems

被引:121
作者
Berry, SM [1 ]
Carroll, RJ
Ruppert, D
机构
[1] Berry Consultants, Sycamore, IL 60178 USA
[2] Texas A&M Univ, Dept Stat, College Stn, TX 77843 USA
[3] Cornell Univ, Sch Operat Res & Ind Engn, Ithaca, NY 14853 USA
关键词
Bayesian methods; efficiency; errors in variables; functional method; generalized linear models; kernel regression; measurement error; nonparametric regression; P-splines; regression splines; SIMEX method; smoothing splines; structural modeling;
D O I
10.1198/016214502753479301
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
In the presence of covariate measurement error, estimating a regression function nonparametrically is extremely difficult, the problem being related to deconvolution. Various frequentist approaches exist for this problem, but to date there has been no Bayesian treatment. In this article we describe Bayesian approaches to modeling a flexible regression function when the predictor variable is measured with error. The regression function is modeled with smoothing splines and regression P-splines. Two methods are described for exploration of the posterior. The first, called the iterative conditional modes (ICM), is only partially Bayesian. ICM uses a componentwise maximization routine to find the mode of the posterior, It also serves to create starting values for the second method, which is fully Bayesian and uses Markov chain Monte Carlo (MCMC) techniques to generate observations from the joint posterior distribution. Use of tire MCMC approach has the advantage that interval estimates that directly model and adjust for the measurement error are easily calculated. We provide simulations with several nonlinear regression functions and provide an illustrative example. Our simulations indicate that the frequentist mean squared error properties of the fully Bayesian method are better than those of ICM and also of previously proposed frequentist methods, at least in the examples that we have studied.
引用
收藏
页码:160 / 169
页数:10
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